基于Lagrangian粒子法的船舶横摇阻尼涡模式数值研究
Numerical Study on Vortex Patterns of Ship Rolling Damping Based on Lagrangian Particle Method

Lagrangian粒子法是近年来新兴的一类无网格方法．基于该广义理论下的有限点法, 将问题求解域离散为有限个空间粒子点, 借助移动最小二乘法获得粒子的物理场函数, 利用投影法分步求解拉格朗日形式下的不可压缩Navier-Stokes方程, 最后数值模拟得到S60船模各二维横剖面在横摇时的涡模式, 有效地捕捉到船体周围流场的非线性特征, 如流体分离、漩涡泄出等．计算结果表明：船舯附近的剖面在横摇时, 在其舭部周围将会产生两个涡, 故舭部表面压力呈正负交错变化; 当剖面位置逐渐靠近船艏或船艉时, 其舭部涡缩减为一个, 此时舭部附近压力符号无变化．将该数值计算结果与试验进行对比验证, 二者吻合较好, 说明Lagrangian观点下的有限点法针对船体各横剖面的横摇阻尼涡模式均给出了较为准确的数值模拟结果, 有效验证了本文计算方法的可靠性．
The Lagrangian particle method，as a new type of meshless method，has attracted much attention in the field of hydrodynamic research recently. Based on the general theory of Lagrangian particle view，the finite point method was studied，which was implemented in such a way that the fluid domain was discretized into a finite number of particles，the moving least square method was introduced for approximating physical field function，and the projection method for solving the incompressible Navier-Stokes equations in Lagrangian form was adopted. The numerical simulation of vortex patterns of two-dimensional cross sections of S60 rolling damping was conducted by the proposed method which effectively depicted the nonlinear characteristics，such as flow separation phenomenon，vortices outflowing and so on. The numerical results show that there are two vortices around midship-like sections and the corresponding pressure sign on rolling surface is changed alternately in different bilges. However，there is only one vortex at the bottom of cross sections near stem or stern，and the sign of pressure maintains consistent. The numerical results and experimental results show good coincidence with each other，which not only illustrates that the finite point method can offer precise simulation results for the vortex patterns of two-dimensional cross sections of ship rolling damping，but also effectively verifies the reliability of the proposed methodology in this paper